WASHINGTON (CNN) -- The White House dismissed a suggestion by a key Republican senator Sunday that it may be time to extend the June 30 deadline for restoring Iraq's sovereignty until the Iraqis are more prepared.

Sen. Richard Lugar of Indiana, chairman of the Foreign Relations Committee, made the suggestion on ABC's "This Week," saying he was "really haunted by the June 30 problem" given persistent violence in Iraq.

"I just see this as a time in which, suddenly, we give sovereignty to somebody," he said. "And now the question is, to who? And how do they secure that?"

He also said the administration should consider sending more troops to Iraq to stabilize the security situation.

Lugar's remarks were made the same day seven U.S. troops were killed in a Baghdad neighborhood in an attack by Shiites angry over the arrest of a top cleric's deputy. Two U.S. Marines were killed elsewhere this weekend. (Full story)

Four U.S. civilian contractors were killed Wednesday in a grenade attack by suspected insurgents in Fallujah, their bodies mutilated afterward by cheering residents. Five U.S. soldiers died the same day in a roadside bombing near Habbaniya. (Full story)

"The United States and our coalition partners are continuing to work closely with Iraqi leaders and the Iraqi people on our plan to meet the June 30 deadline," White House spokesman Brian Besanceney said in response to Lugar's comment.

Besanceney said the United States "will stay in Iraq until the job is done and there is a free, peaceful and democratic Iraq for the Iraqi people."

Lugar told ABC that when the deadline was set for the transfer of power, the thought was "Iraqis wanted this, that they would assume democracy."

"Well, fair enough. But they're at a point in which clearly they can't control the situation," Lugar said.

He said he does not believe the administration has adequately prepared for the aftermath of a power transfer to the Iraqis.

"At this point, I would have thought there would have been a more comprehensive plan, that somebody would have told at least me or somebody else [in the Senate] ... these are the things we're going to do," he said.

"The fact is, we don't know what we're going to do."

Lugar said he plans to hold hearings this month to query administration officials about their plans.

The chairman endorsed an idea floated Sunday by the ranking Democrat on the Foreign Relations Committee, Sen. Joe Biden of Delaware, that Bush convene a summit with European allies on Iraq and ask the U.N. Security Council to appoint a high commissioner to manage Iraq's political transition.

Besanceney said the United Nations and NATO allies were already involved in Iraq.

"The United Nations has a vital role to play in Iraq's future," he said. "Many NATO countries are already participating in our coalition, and we look forward to continuing discussions about ways NATO might be able to help in the future."